Which one has larger kinetic energy: a 500-kg object moving at 40 m/s or a 1000-
ID: 1288426 • Letter: W
Question
Which one has larger kinetic energy: a 500-kg object moving at 40 m/s or a 1000-kg object moving at 20 m/s? How much work would a child do while pulling a 12-kg wagon a distance of 4.3 m with a 22 N force ? A 30-N box is pulled upward 6.0 m along the surface of a ramp that rises at 37 degree above the horizontal. How much work does gravity do on the box during this process? A 0.50-kg toy is attached to the end of a 1.0-m very light siring. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand without breaking is 350 N. What is the maximum speed the mass can have without breaking the string? Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is changed to 4r. What is the magnitude of the new gravitational force?Explanation / Answer
1]
We have the expression for Ke=1/2mv2
Ke of 500 kg object moving with 40 m/s= 1/2* 1000* 2402 = 4*105J
Ke of 1000 kg object moving with 20 m/s= 1/2* 1000* 2402 = 2*105J
500 kg object moving with 40 m/s has the laregre Kinetic energy.
2]
Work= Force * distance
W= F*d= 22N*4.3m=94.6J
3]
Given:-
Weight,W=30N
Distance,d=6m
?=37 degrees
Work done due to gravity, Wg= Force done due to gravity[Fg]*distance[d]
Wg=Fg*d= mgcos?*d=30N*cos[37]*6m=143.75J
4]
Tension of the string balances the centripetal force of the toy
T= Fc
T= mv2/r
V2= T*r/m= 350N*1m / 0.50 kg=700
V= 26.46 m/s
The maximum speed the mass can have without breaking the string is 26.46m/s.
5]
The gravitational force between m and M ,with distance r apart is
FG= GMm/r2
when the masses are changed to 2m and 2M with distance 4r apart is
FG'= G*2M*2m/[4r]2 = GMm/4r2 is the new gravitational energy
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